Steady state thermal fluid flow meters are primarily mass flow based devices, where the rate of heat transfer (dQ/dt) being measured will depend upon the rate of mass flow of the fluid with time (dM/dt) as well as the specific heat capacity at constant pressure (Cp), so that:
            ⅆ      Q              ⅆ      t        ∝            C      p        ⁢                            ⅆ          M                          ⅆ          t                    .      
The volume flow rate (dV/dt) and mass flow rate of the fluid can be related via the density (ρ) such that:
            ⅆ      V              ⅆ      t        =            1      ρ        ⁢                            ⅆ          M                          ⅆ          t                    .      
Many thermal mass flow meters are based on the heat tracer principle. An illustration of a simple version is shown in FIG. 1. In this example, the upstream element (1) and downstream element (2) are temperature sensitive resistors wound around a thin walled pipe (3), which make up one arm of a Wheatstone bridge (4), the other arm being made up of two reference resistors (5). When a voltage is applied across the bridge, the upstream and downstream resistance elements heat up by Joule heating. When no flow is present, the upstream and downstream element thermal losses are matched and a zero volts bridge offset voltage (6) is seen. When fluid flow is present, the downstream resistor thermal losses are less than for the upstream resistor, due to the transfer of heat to fluid by the upstream sensor. The bridge offset voltage will give a voltage signal which will be related to the mass flow rate. This concept can also be used with resistor elements immersed within the sample fluid and also in thin or thick film format. Examples of this type of flow sensor can be seen in patents US2006/0101907, U.S. Pat. Nos. 5,461,913, 4,984,460 and 4,548,075.
A more complex variation on this theme is illustrated in FIG. 2. In this example, a heater coil (10) is centrally wrapped around a thin walled pipe (11), through which the fluid to be measured flows. Two temperature sensors (12) and (13) are mounted equidistantly from the central heater element. Under conditions of no flow, heat transfer to the two temperature sensors will be identical and no temperature difference will be seen. Under conditions of flow, the heat transfer to the downstream temperature sensor (13) will be greater than for the upstream sensor (12), since the fluid will be heated up as it passes by the heater section on its way downstream. The temperature difference between the downstream (Td) and upstream (Tu) sensors can be calibrated for the flow rate, i.e.
            ⅆ      Q              ⅆ      t        ∝      ρ    ⁢                  ⁢          C      p        ⁢                  ⅆ        V                    ⅆ        t              ⁢          (                        T          d                -                  T          u                    )      
This temperature difference will typically be measured by using a Wheatstone bridge circuit (14) where temperature dependent resistors are used to measure Td and Tu in one arm of the bridge, external reference resistors (15) are used in the other arm of the bridge and the output voltage measured across the bridge (16) is related to fluid flow rate. This design and the previous format are often used in conjunction with solenoid valves for mass flow controllers.
However, as for the previously described method, it is not an energy efficient means for measuring the flow rate and is mainly used for gases at low flow rates, often in a bypass arrangement. An alternative mechanical arrangement of this design with higher sensitivity is to mount the heating and sensing elements in the sample stream within the pipe, however, it is much more difficult to accurately and repeatably position the elements within the pipe bore and the elements' performance may be significantly affected by high sample stream velocity, particulates or entrained fluids condensing out. This can also be used in thin or thick film format. Examples of using such a method are shown in patents U.S. Pat. Nos. 4,651,564 and 7,255,001. Such an example can also be used to measure the velocity of a fluid flow by pulsing the central heater element and measuring the time of flight or phase shift for the heat pulse to reach the downstream element, with the upstream element acting as a reference to cancel common mode heating effects when required. The velocity can be found from the distance between the heater and sensing element divided by time of flight. An example of such a device can be seen in patent U.S. Pat. No. 6,169,965 and a general device for measuring time of flight in fluids via a thermal pulse is shown in U.S. Pat. No. 5,347,876.
The flow velocity, which can be related to fluid flow rate, can also be measured via the cooling by the flow of a fluid over a hot element or filament wire, such as a hot wire anemometer, an illustration of which is shown in FIG. 3. In this case, the hot measurement element (20) positioned within a pipe (21) is cooled convectively by the fluid passing over it and the decrease in element temperature or increase in power required to maintain the same working temperature constitutes the signal. A Wheatstone bridge (22) may be used to output the signal, where the hot element consists of a temperature dependent resistor, with reference resistors (23) making up the other bridge resistances. The offset voltage across the bridge (24) is related to the fluid flow rate. Often this type of device is used in conjunction with a reference temperature sensor immersed in the sample fluid in order to maintain a fixed uplift temperature of the active measurement resistive element relative to the ambient fluid temperature. Examples are shown in patents US2008/0271545, US2005/0150310 and U.S. Pat. No. 5,780,737.
Thin filament wires or thin film devices will give fast time responses and large signals when compared to thicker wires, but they are fragile and will be subject to error if there are particulates or entrained fluids within a gaseous mixture which could deposit on the wire. They also have limited flow ranges unless used in bypass mode.